Israel Journal of Mathematics

, Volume 54, Issue 3, pp 301–306 | Cite as

On the ergodicity of a class of skew products

  • P. Hellekalek
  • G. Larcher


Letϕ: [0, 1]→R have continuous derivativeon the closed interval [0, 1], ∫ 0 1 ϕ(x)dx=0, and letα be irrational. Ifϕ(1) ≠ϕ(0), then (x, y) ↦ (x + α, y + ϕ (x)) is ergodic onR/Z ×R.


Closed Interval Irrational Number Closed Inter Continue Fraction Expansion Normalize Haar Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. Anzai,Ergodic skew product transformations on the torus, Osaka Math. J.3 (1951), 83–99.zbMATHMathSciNetGoogle Scholar
  2. 2.
    J. P. Conze,Ergodicité d’une transformation cylindrique, Bull. Soc. Math. France108 (1980), 441–456.zbMATHMathSciNetGoogle Scholar
  3. 3.
    H. Furstenberg,Strict ergodicity and transformations of the torus, Amer. J. Math.83 (1961), 573–601.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    P. Hellekalek,Ergodicity of a class of cylinder flows related to irregularities of distribution, to appear in Comp. Math.Google Scholar
  5. 5.
    L. Kuipers and H. Niederreiter,Uniform Distribution of Sequences, John Wiley & Sons, New York, 1974.zbMATHGoogle Scholar

Copyright information

© Hebrew University 1986

Authors and Affiliations

  • P. Hellekalek
    • 1
  • G. Larcher
    • 1
  1. 1.Institut für MathematikUniversitat SalzburgSalzburgAustria

Personalised recommendations